This probably isn't of much help, but I'm currently doing an internship in medical stats/research (strongly related to health psychology) and we've had talks from a number of people from KCL, so I imagine it is a very strong department. While I imagine they're both equally as good, UCL does carry a better world-wide reputation than KCL imo, and it is one of the best or the best for psychology in this country. Sorry if this adds very little to your brain-storming.